This proposal is for a study of nonparametric Bayesian estimation and testing procedures for randomly right censored data arriving in survival studies. Special emphasis will be on those decision problems in which there is a prior distribution on the space of all distribution functions on the real line. The problems can be thought of as Bayes versions of the fundmental work of Ferguson (and also of Doksum) on the Dirichlet process prior distribution and its natural generalizations. As our primary application, we hope to extend some of our earlier results on the Bayes estimation and comparison of survival curves which occur in life table methods applicable to cancer data wherein the observations are censored randomly on the right. We plan to study the large and small sample properties of the Bayesian survival curve estimator we have obtained and compare these properties with the usual estimators in the non-Bayesian case. Besides the Bayes problem we intend to consider certain related empirical Bayes problems which are natural analogs of the Bayes problems solved. In this regard, we have already obtained an estimator of survival curves whose properties we have to examine in more detail. One such interesting property we have already derived is that the estimator is a Bayesian generalization of the much used Kaplan-Meier survival curve estimator.